Problem: Surveying Astronomy: The Equation of Time

Problem: Surveying Astronomy: The Equation of Time

An hour measured by the apparent motion of the true sun, which is sundial time, varies with the time of year. An hour measured by the imaginary mean sun is constant throughout the year. Which of the following reasons account for this effect?

(A) The orbit of the earth around the sun is elliptical. Therefore, the apparent motion of the true sun is more rapid when the earth is closer to the sun and slower when the earth is farther away.
(B) The apparent motion of the true sun is along the ecliptic and the motion of the imagined mean sun is along the celestial equator. Therefore, the mean sun moves steadily in terms of right ascension, which the true sun does not.
(C) The tidal forces of the moon and other planets of the solar system cause the rate of the rotation of the earth on its axis to vary significantly during the year. This variation causes the apparent motion of the true sun to vary.
(D) Both A and B are true.

This is problem 76(4-43) from the new second edition of 1001 Solved Surveying Problems by Jan Van Sickle. Reprinted with permission from 1001 Solved Surveying Problems by Jan Van Sickle (1997, 728 pp., Professional Publications Inc.). For details on this and other FLS exam-prep books, call 800/426-1178 or visit www.ppi2pass.com .

Answer: D

According to Kepler’s law of planetary motion, the earth moves more rapidly along its orbital path at perihelion and more slowly at aphelion. While this accounts for some variation in the motion of the true sun through the sky, it is not the largest factor. The true sun appears to move along the ecliptic due to the inclination of the earth’s axis with respect to its orbital plane with the sun. Therefore, it does not move in right ascension at a constant rate as does the mean sun. the mean sun is imagined to move steadily in right ascension along the celestial equator.